Need Help Calculating and Implementing Cs - Wright's Index

S

SPC_Newbie

#1
Hello,

I've played with some data in a speadsheet but have no idea if I've even come close to to calculating Cs properly.

I also don't know what a good number looks like - woul it be similar to Cp, meaning am I looking for a 1.33 or better? How would we calculate control limits?

Does anyone have a spreadsheet that does the calculation? I'm very interested in any known test data and results someone might have so I can prove out my sheet/calculations.

I'm using the calculation: Cs = min{USL - Mean, Mean-LSL}/{3*[sigma^2+(Mean-Target)^2+abs(3rd_Moment/sigma)]} (thanks Darius!)

Attached is my worksheet. Am I even close??

I kind of put it together leveraging information from a you tube video as this formula is my first introduction to moments/skew/kurtosis:


SIDE NOTE: I've searched for an article I had been pointed to before (EVALUATION OF PROCESS CAPABILITY INDEX FOR NON-NORMAL DISTRIBUTIONS) but have not turned it up.
 

Attachments

Elsmar Forum Sponsor

Stijloor

Staff member
Super Moderator
#2
Hello,

I've played with some data in a spreadsheet but have no idea if I've even come close to to calculating Cs properly.

I also don't know what a good number looks like - would it be similar to Cp, meaning am I looking for a 1.33 or better? How would we calculate control limits?

Does anyone have a spreadsheet that does the calculation? I'm very interested in any known test data and results someone might have so I can prove out my sheet/calculations.

I'm using the calculation: Cs = min{USL - Mean, Mean-LSL}/{3*[sigma^2+(Mean-Target)^2+abs(3rd_Moment/sigma)]} (thanks Darius!)

Attached is my worksheet. Am I even close??

I kind of put it together leveraging information from a you tube video as this formula is my first introduction to moments/skew/kurtosis:


SIDE NOTE: I've searched for an article I had been pointed to before (EVALUATION OF PROCESS CAPABILITY INDEX FOR NON-NORMAL DISTRIBUTIONS) but have not turned it up.
A quick bump.

Can someone help?

Thank you very much!!

Stijloor.
 
D

Darius

#3
Well, close enought :D......

I changed a little your file, sorry a little bit messy, but it show the idea.

Control limits, are a different issue.

I try to show you a way, it's not documented:nope:, but I think is a handy way to do it.:bigwave:
 

Attachments

S

SPC_Newbie

#4
What a fantastic reply, I know it took some time to evaluate and correct my sheet - I was really stuck - Mil Gracias!

I'm going through it now, trying to make sure I understand. It'll be a little while before I know what I need to ask more about.:tg:

Thanks Again!!
 
S

SPC_Newbie

#5
OK, Partially digested!!

I have a big question or two, a small one and an observation.

First Big One: I was under the impression that Cs is an index I can use that rewards values closer to the target, in my case 0 (think flatness, parallelism, etc). I simply raised my USL and expected that my Cs would be better. It did not change. I see the the third moment/sigma doesn't take into account USL (near as I can tell). I'm pretty sure this third moment/sigma value is referred to as skew and is what differentiates Cs from Cpmk. Also, looking through the equations, where USL is used, min(USL-mean, Mean-LSL), it is not coming up as the minimum value so is not used. What am I missing?

The next kind of Big one: How/why did the values .68 and .95 get chosen in the DS_up and Ds_dwn calculations?

Small question: what does np stand for in the terms np_UCL and np_LCL

Observation: Kind of cool how the moments are pretty much calculated like a typical Standard deviation, the difference being we don't take the SQRT of the value.

Thank you!
 
D

Darius

#6
“I simply raised my USL and expected that my Cs would be better. It did not change. I see the third moment/sigma doesn't take into account USL (near as I can tell).”
:2cents:Well maybe, just because, the minimum value is domed is this case to be depending from the LSL, maybe, if is no possible the 0, it should not be considered. I will do some tests and tell you my conclusions.

:popcorn:0.68 and 0.95 are the values for “bell shaped” distribution, 68% of the data are between +/- 1 sigma, the 95% of the data are between +/-2 sigma. I know is used in this case for non parametrics (it can be called half-parametrical method).:lol: The method I outlined take the distribution in two halves (using the median), and the ds_up is calculated as it was a normal distribution but taking just one side in account at the time (for ds_up the upper side, for ds_dwn the lower ones). It may sound weir but I worked with it and found it to work fine for me, I saw sometime ago a method that used the percentile for the percentage at +/- 3 sigma to determine the control limits (ones again …, a half-parametrical method), and it can be done that way, but for data with many “outliers”, found this method more robust (the outliers doesn't have any effect). As I told you is a method I tested (and created), you can simulate data that behave as gamma and work fine. I even use it for outlier detection on a "modificated chauvenet" (by me),method.

np in this case, sorry…, is non parametrical.
 
D

Darius

#7
As I spected, as other capability indexes, it take the minimum of upper or lower, but in your case there not seem to be a lsl because is a "natural limit"

You can change the file in two ways (both gave the same results)
first:
clear LSL => d11
change d14 to

=+MIN(IF(D10="",999,D10-D6),IF(D11="",999,D6-D11))/(3*(D13^2+(D6-D12)^2+N10/D13)^0.5)

or

Second:
=+(D10-D6)/(3*(D13^2+(D6-D12)^2+N10/D13)^0.5)

And enjoy your self, changing USL.

Take your time, we will be here...
 
S

SPC_Newbie

#8
OK Darius, I will give these a try and see how they look.Thanks for encouraging me that I still have support :thanks:.

Cheers!!
 
S

SPC_Newbie

#9
:applause:Works great! Thank you very much!!

So now I can see my Cs numbers improving as I increase USL, how do I know what is a good number? What I'm trying to say is what number(s), if any, am I aiming for - do we have a threshold or target Cs?

Getting so close!!
 
Thread starter Similar threads Forum Replies Date
J Need help calculating actual Ppk - Result of % GR&R=11.8% when conducting MSA Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 11
D Need Help on the method of calculating tube wall Within Part Variation Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 7
R Need help on calibration result analysis Measurement Uncertainty (MU) 14
G Need Help with Run @ Rate for Medical Devices ISO 13485:2016 - Medical Device Quality Management Systems 0
F Need help in IMS management review Management Review Meetings and related Processes 3
S I need help in corrective action plan Nonconformance and Corrective Action 15
D Weird spec sheet - need help Measurement Uncertainty (MU) 3
K Need Help With Auditing Suppliers Against ISO 9001 ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 50
R Lead auditor scenario (Need help) is this non conforming to ISO13485 Manufacturing and Related Processes 2
U Need Help With API Q2 Quality Manual Oil and Gas Industry Standards and Regulations 8
D Need some Help on 8D fault tree analysis Problem Solving, Root Cause Fault and Failure Analysis 6
K Screen printing ink and machine selection_ Need help Manufacturing and Related Processes 6
J Need Help with FPY Data in Assembly Process Manufacturing and Related Processes 7
S Need help on "Country of Origin" Medical Device and FDA Regulations and Standards News 0
M Need Help With Information Security Asset Risk Register IEC 27001 - Information Security Management Systems (ISMS) 2
C ISO/ IEC 17021 Resource requirement (need help) Document Control Systems, Procedures, Forms and Templates 5
SocalSurfer AS9100 new certificate, but need QMS software, help Quality Assurance and Compliance Software Tools and Solutions 2
S Need help with analysing a survey on minitab Using Minitab Software 1
K A proposal for the model Quality Management - I need help for the project ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 3
R Probability - Need a help to solve the below question Statistical Analysis Tools, Techniques and SPC 5
8 Need Help - Runout - Function Gage Inspection, Prints (Drawings), Testing, Sampling and Related Topics 7
S New to FAIR, need help in filling it out AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 8
R Pls help --- Need expert advice on Video Measurement Measurement Uncertainty (MU) 0
Ajit Basrur Need help to understand HIPAA requirements ISO 13485:2016 - Medical Device Quality Management Systems 17
Z I need help with getting a CFS in China Manufacturing and Related Processes 2
S Need help wrapping my head around confidence vs beta error Statistical Analysis Tools, Techniques and SPC 2
P Received a minor for not having good measureables/goals. Need help with KPIs. IATF 16949 - Automotive Quality Systems Standard 52
A Failed the AS9120B Exam Twice.....Need Help AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 11
Ajit Basrur Need help in Conditional Formatting for the entire row Excel .xls Spreadsheet Templates and Tools 3
H Need help on Quality Improvement Plan (QIP) Quality Tools, Improvement and Analysis 5
S Help: Need Control Self Assessment Questionnaire for HR Departmental Functions Process Audits and Layered Process Audits 0
M Need help in Calibration of Directional Coupler General Measurement Device and Calibration Topics 2
L Need HELP with Internal Audit Program ISO 13485.2003 Quality Management System (QMS) Manuals 3
J Supporting Processes - Internal Audits - Need help settling a debate IATF 16949 - Automotive Quality Systems Standard 4
A Cpk Formula seems off, need help!? Capability, Accuracy and Stability - Processes, Machines, etc. 11
A Need Help With AEA Auditor Related Situational Questions AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 1
E Transformer Overload Test - Need help IEC 60601 - Medical Electrical Equipment Safety Standards Series 3
C I Need Help with Drafting Conventions!!! Design and Development of Products and Processes 4
M Need help on QMS Development in an AS9100C certified organization AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 10
R Need Help on Analysis: How to know potential causality model from historical data Problem Solving, Root Cause Fault and Failure Analysis 5
B Need help tracking training for my business Quality Assurance and Compliance Software Tools and Solutions 3
B Need help with a Control Plan for Encapsulation Mold / Trimming / Forming Tooling FMEA and Control Plans 9
S I need help from all of you bros Oil and Gas Industry Standards and Regulations 1
LRE67 Need help identifying this "thing" Coffee Break and Water Cooler Discussions 9
G Need help on Device Description in the Acceptance Checklist for Traditional 510(k) Other US Medical Device Regulations 2
K Need help finding a book on Documentation Book, Video, Blog and Web Site Reviews and Recommendations 8
J Need help/advice on video editing software etc..... Coffee Break and Water Cooler Discussions 8
L Need Help with Case Study Questions Manufacturing and Related Processes 16
W Help explaining the need for the Process Approach AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 4
Ron Rompen Unusual problem with Excel - Need some help Excel .xls Spreadsheet Templates and Tools 7

Similar threads

Top Bottom